8 Rates

Internal structures of samples and shear-thinning behavior

The terms “shear-thinning” and “pseudoplastic flow behavior” are synonyms. This behavior is characterized by decreasing viscosity with increasing shear rates, caused by the samples internal structure. Typical materials that show this behavior are coatings, glues, shampoos, polymer solutions, and polymer melts.

Polymers

Figure 1: Filamentary molecules of a polymer solution or polymer melt: Left: At rest with coiled and entangled molecules. Right: In motion under shear, stretched and partly disentangled molecules, oriented in the direction of shear.

At rest, long, filamentary molecules of uncrosslinked polymers contract to form balls. At the edges of the molecules, the chains become entangled with each other (Figure 1). Under shear, the entangled balls change their shape and become ellipsoid (shaped like an American football or an airship). This deformation goes hand in hand with increasing disentanglement of the molecules. As individual molecules have less flow resistance than entangled superstructures, the result is shear-thinning flow behavior with decreasing viscosity values at higher shear rates.

Coiled molecules at rest have a so-called hydrodynamic diameter of between 5 nm and 50 nm. Example: The size ratio for polyethylene (PE) of molar mass M = 100 kg/mol, with filamentary molecules of approximate length L = 1 μm = 1000 nm (when stretched) and diameter of approx. d = 0.5 nm, is L/d = 2000:1. For a better understanding, just imagine one spaghetti noodle which is 1 mm thick and 2000 mm = 2 m long.

Suspensions containing needle-shaped or platelet-like particles

Figure 2: Needle-shaped or platelet-like particles in a suspension: Left: Randomly arranged at rest. Right: In motion under shear, oriented in the direction of shear.

In the absence of interaction forces, the particles in a suspension at rest are oriented randomly (Figure 2). When shear is applied, the particles start to align themselves parallel to the direction of flow. This facilitates their sliding along each other more easily. Since the individual particles now show less flow resistance than they do in an unordered state at rest, it is obvious that with increasing shear rate they display shear-thinning flow behavior with a decrease in viscosity. 

Example 1: Pigment particles in metallic-effect automotive coatings, so-called aluminum flakes, have a diameter of d = 7 to 30 μm and a thickness of h = 0.2 μm to 1 μm: The resulting ratio d/h is 30:1. For a better understanding: Beer mats have a shape like this. Example 2: Ceramic primary particles in casting slurries such as montmorillonite (e.g. bentonite) are approx. 800 nm long, 800 nm wide, and 1 nm thick.

Suspensions with superstructures of agglomerated primary particles

Figure 3: Particles in a suspension: Left: Agglomerated particles at rest. Right: Under shear, in motion with breakdown of the superstructure. This reduces the flow resistance, thus causing shear-thinning flow behavior.

At rest, agglomerates in a suspension also enclose parts of the dispersion liquid thus immobilizing it (Figure 3). Under shear, the superstructures increasingly disintegrate into primary particles, or, to be more precise, into their aggregates. As the smaller superstructures display less flow resistance, and as the formerly immobilized dispersion liquid is now free to move again, the result is shear-thinning flow behavior with decreasing viscosity at increasing shear rates.

Primary particles have a size of 1 nm to 10 nm, while aggregates, with a total size of up to 100 nm, are primary particles linked with relatively strong bonds. Agglomerates, with an overall size of up to 100 μm, are characterized by relatively loose bonds; they consist of aggregates or particles.

Emulsions with dispersed droplets

Figure 4: Droplets in an emulsion. Left: State at rest with sphere-like droplets. Right: In motion under shear, the droplets are deformed in the direction of shear. Droplets and fat particles in milk have diameters of between 0.1 μm and 10 μm.

At rest, the droplets in an emulsion are shaped like spheres (Figure 4). When flowing, the size and shape of the droplets are dependent on the shear applied. Increasing deformation leads to an ellipsoid shape. Because the droplets now show a smaller cross section in the direction of flow, the emulsion displays a decrease in viscosity, i.e. shear-thinning flow behavior.

Note: Emulsions with broken droplets under strong shear. It is possible that, under high shear, subdivision of droplets may occur, resulting in increased viscosity. The cause may be the increased volume-specific surface that accompanies the breakdown of the droplets. If strong interaction forces are present at the interface between the two liquid phases, this may cause undesired results. For example, a hand cream or lotion may feel sticky, tacky, or stringy when applied. An interesting option for optically displaying transparent substances under defined shear conditions is the use of a rheo-microscope (Figure 5).

Figure 5: Emulsion composed of water droplets in silicone oil, viewed under an optical microscope. (1) At rest, the droplets are sphere shaped; (2) At a low shear rate of 0.5 s-1, the droplets of the inner phase are slightly deformed; (3) At a shear rate of 16 s-1, clearly deformed droplets are now shaped like ellipsoids (like an airship); (4) At rest after having been subjected to a high shear rate of 100 s-1, which has resulted in a breakdown of droplets and a clearly reduced mean droplet size.